Quadratic Equations Set – 29

1. I. 2x2+25x + 78 = 0,
II. 3y2 + 23y + 30 = 0
A) If x > y
B) If x < y
C) If x ≥ y
D) If x ≤ y
E) If x = y or relation cannot be established

Answer & Explanation

 Option D
Solution: 

2x2+ 25x + 78 = 0,
2x2+12x + 13x + 78 = 0
Gives x = -13/2, -6
3y2 + 23y + 30 = 0
3y2 + 18y + 5y + 30 = 0
Gives y = -6, -5/3
Put all values on number line and analyze the relationship
-13/2…. -6….-5/3

 

2. I. 2x2 + 7x – 15 = 0,
II. 3y2 + 11y ¬– 20 = 0
A) If x > y
B) If x < y
C) If x ≥ y
D) If x ≤ y
E) If x = y or relation cannot be established

Answer & Explanation

 Option E
Solution: 

2x2 + 7x – 15 = 0
2x2 + 10x – 3x – 15 = 0
Gives x = -5, 3/2
3y2 + 11y ¬– 20 = 0
3y2 + 15y ¬– 4y – 20 = 0
Gives y = -5, 4/3
Put all values on number line and analyze the relationship
-5.…. 3/2….4/3
When x = 3/2, it is both > y(-5) and < y(4/3)

 

3. I.3x2– 11x + 6 = 0,
II. 3y2 + 11y ¬– 20 = 0
A) If x > y
B) If x < y
C) If x ≥ y
D) If x ≤ y
E) If x = y or relation cannot be established

Answer & Explanation

 Option E
Solution: 

3x2– 11x + 6 = 0
3x2–9x – 2x + 6 = 0
Gives x = 2/3, 3
3y2 + 11y ¬– 20 = 0
3y2 + 15y ¬– 4y – 20 = 0
Gives y = -5, 4/3

 

4. I.3x2 + 17x + 20 = 0,
II. 3y2– 4y – 15 = 0
A) If x > y
B) If x < y
C) If x ≥ y
D) If x ≤ y
E) If x = y or relation cannot be established

Answer & Explanation

 Option D
Solution: 

3x2 + 17x + 20 = 0
3x2 + 12x + 5x + 20 = 0
Gives x = -4,-5/3
3y2– 4y – 15 = 0
3y2– 9y + 5y – 15 = 0
Gives y= -5/3, 3

 

5. I. 5x2– 19x + 12 = 0,
II. 5y2 +6y – 8 = 0
A) If x > y
B) If x < y
C) If x ≥ y
D) If x ≤ y
E) If x = y or relation cannot be established

Answer & Explanation

 Option C
Solution: 

Explanation:
5x2 – 19x + 12 = 0
5x2 – 19x + 12 = 0
Gives x = 4/5, 3
5y2 + 6y – 8 = 0
5y2 + 10y – 4y – 8 = 0
Gives y= -2, 4/5

 

6. I.3x2– 10x – 8 = 0,
II. 2y2 + 13y + 21 = 0
A) If x > y
B) If x < y
C) If x ≥ y
D) If x ≤ y
E) If x = y or relation cannot be established

Answer & Explanation

 Option A
Solution: 

3x2– 10x – 8 = 0
3x2– 12x + 2x – 8 = 0
Gives x = -2/3, 4
2y2 + 13y + 21 = 0
2y2 + 6y + 7y + 21 = 0
Gives y = -7/2, -3

 

7. I. 4x2–15x + 9 = 0,
II. 2y2 – 15y + 27 = 0
A) x > y
B) x< y
C) x ≥ y
D) x ≤ y
E) x = y or relationship cannot be determined

Answer & Explanation

 Option D
Solution: 

4x2 –15x + 9 = 0
4x2 –12x – 3x + 9 = 0
Gives x = 3/4, 3
2y2 – 15y + 27 = 0
2y2 – 6y – 9y + 27 = 0
So y = 3, 9/2

 

8. I. 3x2 –14x + 8 = 0,
II. 2y2 – 3y ¬– 20 = 0
A) x > y
B) x< y
C) x ≥ y
D) x ≤ y
E) x = y or relationship cannot be determined

Answer & Explanation

 Option E
Solution: 

3x2 –14x + 8 = 0
3x2 –12x – 2x + 8 = 0
Gives x = 2/3, 4
2y2 – 3y ¬– 20 = 0
2y2 – 8y + 5y ¬– 20 = 0
So y = -5/2, 4
When x = 2/3, x > y(-5/2) and also x < y (4), so relationship cannot be determined

 

9. I. 4x2– (1– 8√2)x– 2√2 = 0
II. 5y2 + (1 + 5√2)y + √2 = 0
A) If x > y
B) If x < y
C) If x ≥ y
D) If x ≤ y
E) If x = y or relation cannot be established

Answer & Explanation

 Option E
Solution: 

4x2– (1 – 8√2)x – 2√2 = 0
(4x2 – x) + (8√2x – 2√2) = 0
x (4x – 1) + 2√2 (4x – 1) = 0
So x = 1/4, -2√2 (-2.82)
5y2 + (1 + 5√2)y + √2 = 0
(5y2 +y) + (5√2y + √2) = 0
y (5y + 1) + √2 (5y + 1) = 0
So, y = -1/5 (-0.2), -√2 (-1.4)

 

10. I. 3x2– (9 + √3)x + 3√3 = 0,
II. 3y2– (3 + 3√3)y + 3√3 = 0
A) x > y
B) x< y
C) x ≥ y
D) x ≤ y
E) x = y or relationship cannot be determined

Answer & Explanation

 Option E
Solution: 

3x2– (9 + √3)x + 3√3 = 0
(3x2 – 9x) – (√3x – 3√3) = 0
3x (x – 3) – √3 (x – 3) = 0,
So x = 3, √3/3 (0.58)
3y2– (3 + 3√3)y + 3√3 = 0
(3y2 – 3y) – (3√3y – 3√3) = 0
3y (y – 1) – 3√3 (y – 1) = 0
So x = 1, √3 (1.73)

Leave a Comment

Your email address will not be published.